The correct answer is **B)
for
**.Mathematical induction is a proof technique used to establish the truth of a statement for all natural numbers (or a subset starting from a specific number). It involves two steps:1. **Base Case:** Prove the statement is true for the smallest value of *n* (in this case, n=5).2. **Inductive Step:** Assume the statement is true for some arbitrary value *k* (the inductive hypothesis), and then prove it's also true for *k+1*.Let's see why the other options aren't suitable for mathematical induction:* **A) √2 is an irrational number:** The proof of the irrationality of √2 typically uses proof by contradiction, not mathematical induction.* **C) ax² + bx + c = 0 has real solutions if b² - 4ac ≥ 0:** This is a statement about the nature of solutions to a quadratic equation. While the quadratic formula itself can be proven, the statement about real solutions isn't something that lends itself to a proof by induction. Induction works best with statements that involve a variable representing a natural number and a recursive relationship.Only option B fits the structure needed for a proof by mathematical induction. We can prove it by showing it's true for n=5 (base case) and then assuming it's true for n=k and proving it for n=k+1 (inductive step).